Integrand size = 24, antiderivative size = 24 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\text {Int}\left (\frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3},x\right ) \]
[Out]
Not integrable
Time = 0.07 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx \\ \end{align*}
Not integrable
Time = 5.53 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx \]
[In]
[Out]
Not integrable
Time = 30.57 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92
\[\int \frac {1}{x^{3} \arctan \left (a x \right )^{3} \sqrt {a^{2} c \,x^{2}+c}}d x\]
[In]
[Out]
Not integrable
Time = 0.24 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.54 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int { \frac {1}{\sqrt {a^{2} c x^{2} + c} x^{3} \arctan \left (a x\right )^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 6.17 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int \frac {1}{x^{3} \sqrt {c \left (a^{2} x^{2} + 1\right )} \operatorname {atan}^{3}{\left (a x \right )}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.35 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int { \frac {1}{\sqrt {a^{2} c x^{2} + c} x^{3} \arctan \left (a x\right )^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 94.41 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.12 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int { \frac {1}{\sqrt {a^{2} c x^{2} + c} x^{3} \arctan \left (a x\right )^{3}} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.50 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x^3 \sqrt {c+a^2 c x^2} \arctan (a x)^3} \, dx=\int \frac {1}{x^3\,{\mathrm {atan}\left (a\,x\right )}^3\,\sqrt {c\,a^2\,x^2+c}} \,d x \]
[In]
[Out]